Poincaré’s inequalities and Talagrand’s concentration phenomenon for the exponential distribution |
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| Authors: | S Bobkov M Ledoux |
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| Institution: | (1) Department of Mathematics, Syktyvkar University, 167001 Syktyvkar, Russia , RU;(2) Département de Mathématiques, Laboratoire de Statistique et Probabilités associé au CNRS, Université Paul-Sabatier, F-31062 Toulouse, France, FR |
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| Abstract: | Summary. We present a simple proof, based on modified logarithmic Sobolev inequalities, of Talagrand’s concentration inequality for
the exponential distribution. We actually observe that every measure satisfying a Poincaré inequality shares the same concentration
phenomenon. We also discuss exponential integrability under Poincaré inequalities and its consequence to sharp diameter upper
bounds on spectral gaps.
Received: 10 June 1996 / In revised form: 9 August 1996 |
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| Keywords: | Mathematics Subject Classification: Primary: 60E15 28A35 60E99 Secondary: 58C40 |
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